Question

I will pick your answer as brainlist !!
a company that manufactures smartphone cases plans to increase production by an additional 120 cases each month for the next 24 months. last month they manufactured 1930 smartphone cases

A. would an arithmetic sequence give the total number of smartphone cases made this year? Explain

B. what is the arithmetic sequence that models the company's monthly output?

C. how many smartphone cases does the company plan to produce during the next 24 months

Answer 1

Using arithmetic sequence concepts, it is found that:

a) Yes, it is an arithmetic sequence. as the common difference is constant.

b) The sequence is: $a_n = 120n + 1930$

c) The company plans to produce 82,320 cases during the next 24 months.

What is an arithmetic sequence?

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

$a_n = a_1 + (n - 1)d$

In which $a_1$ is the first term.

The sum of the first n terms is given by:

$S_n = \frac{n(a_1 + a_n)}{2}$

Item a:

The production will be increased  by an additional 120 cases each month for the next 24 months, which means that the common difference is constant, so yes, it is an arithmetic sequence.

Item b:

• Last month they manufactured 1930 smartphone cases, hence in this month they will manufacture 2050 cases, hence $a_1 = 2050$.

• Increases by 120 a month, hence $d = 120$.

Then, the sequence is:

$a_n = a_1 + (n - 1)d$

$a_n = 2050 + 120(n - 1)$

$a_n = 120n + 1930$

Item c:

$a_1 = 2050$

$a_24 = 120(24) + 1930 = 4810$

Then:

$S_{24} = 12(2050 + 4810) = 82320$

The company plans to produce 82,320 cases during the next 24 months.

You can learn more about arithmetic sequence concepts at https://brainly.com/question/26053884